Mathematics all-in-one cheat-sheet (2013) [pdf] | Hacker News Reader

Mathematics all-in-one cheat-sheet (2013) [pdf]

ourway.keybase.pub

1,060 pointsrodmena161 comments

I think the author's page (Alex Spartalis) deserves to be mentioned:

https://www.alexspartalis.com/cheat-sheet.html

He has the same version (v2.10) there and mentions that, "The Web version does not include the distribution functions due to file size restrictions. Email me if you would like a copy of these." That explains why pages 213-330 are missing. Someone should offer to upload the full copy to keybase.pub (or someplace) since his personal site can't handle the load.

People sometimes do tremendous work creating a program/book/artwork, and want the world to see it, but don't get around to really share it or promote it.

It'd be nice if there was a cheat sheet for Category Theory as well. I thought that part could be found in the link you provided, but seems like the author hadn't (2013) included CT in this almanac.

I sent a message using the contact form. Thanks for mentioning this.

If you do end up reuploading it, please look into fixing all the typographical issues too. Ty!

If you do re-upload it, you should let us know here and/or post a link to the full version on HN.

Just use torrent! It's easy, and potentially free!

Distributing new versions is an issue though, as there is no way to tell anyone who is currently seeding the old torrent. But it's not a terrible idea if it turns out there is really a lot of bandwidth (I don't expect that), then I could use my server for seeding at least.

Hmm, that sounds like an interesting problem in itself, a torrent client that handles versioning and updates behind the scenes.

I mean, thats essentially the apple app store right? Just with torrents and documents instead of apps? So like a freely distributed google docs, but for everything. That movie you downloaded a week ago got a better version, the sci-hub article you downloaded last week has commentary from the author or has been disputed, That microsoft office (excel, word, onenote) you've been working on with a group has a long revision history and automatic version control. You could even download the 'latest version' at 'run-time'; when you double click to open the document. There's a company, or atleast the very start of one in these ideas.

Isn't that already solved with RSS?

RSS is widely used to publish new pirated tv show episodes already, so that your torrent client can fetch them automatically when they're available.

This is a solved problem, RSS is used to automatically fetch new pirated tv show episodes.

For some reason v2.10 incorrectly shows e^1pi instead of e^ipi in the Euler equation. v2.6 is correct.

I believe that's an iota (ι) not a 1.

Wow, I have to say I feel somewhat bad for the author who spent so much time (months?) compiling this semi-comprehensive reference work. There's so much information, but at the same time, so little useful information to any particular reader. It's so broad as to be a hindrance to using it in any sort of daily reference.

Who would use this? Wouldn't you probably resort to a reference more specific to your field?

Is this the product of someone's superficial fascination with mathematical equations combined with OCD to copy down everything ever read, gone awry? Or is this like a strange version of a Noah Webster?

This comment reminds me of the archetypal high-school student who asks "when are we ever going to use this stuff?"

If you have to ask...

I'm hoping that this work might give me some valuable info on how to get started on various Project Euler[0] problems that I might otherwise have no idea how to approach, or that I wouldn't know what area of math to do research for.

[0]https://projecteuler.net/

This is exactly what I thought. In fact, when I got to the section that listed the right-truncatable primes, I immediately searched Euler because I knew there was a problem about them -- turns out I had already solved it though lol.

Well, I find it extremely useful.

This is my new go-to item when someone asks me, "What would you bring with you if you could go back in time to the year 1600?"

I thought I was the only one who pondered that! I think we'd have even more fun times in 1st century CE Alexandria.

They'd burn you at the stake.

This comment got me thinking: if that were to happen unexpectedly, how would you

1) determine when and where you were, and

2) convince the locals who probably don't speak your language or look like you not to kill or imprison you?

3) Live for more than a few days, with bacterial fauna of that time being so different, your immune system, completely unpolished for those type of bugs, would probably hold out for only a very short time.

Your immune system carries memories of those days.

With antibiotics prevalent that memory may be fuzzy

Wouldn't a book on microbiology be much more useful to humanity?

I have a copy of The Handbook of Mathematics, which is kind of a similar idea done commercially. It's genuinely useful, but the thing is that it's HUGE, well over 1000 pages. The main reason for this is that it is organized and fairly comprehensive, it's more of a reference than a cheat sheet. It has enough detail and depth that you can actually count on it to remind you of a subject you haven't had to use in a while.

The post here is really more like a true cheat sheet. Random topics and formulas thrown together without much organization or depth. You need to remember quite a lot already to be able to actually make use of any of this information, which to me kinda defeats the purpose. Another big problem is consistent and well-defined notation. This looks like it's copied and pasted from a lot of different sources, so you are going to have a bunch of different notational conventions that you will need to be conscious of.

My advisor had material of this sort (eg lots of Runge Kutta schemes and theorems about RK conditions; also books of ODE/PDE solutions. It came useful when we were working intensively toward the end of my thesis.

Cheat-sheet we were allowed to use during math exams at university:

Theoretical Computer Science Cheat Sheet https://www.tug.org/texshowcase/cheat.pdf

It's 10 pages, so 3 papers with one page free for something that might be missing.

I often used this when solving assignments and can recommend it to any computer science student.

Making your own cheat sheet is half the battle when you are trying to learn the topic. I remember in my 4th year Stochastic Processes class [0] (back in 2005, wow) we could bring in a double sided page of notes. I wrote my sheet up in LaTeX [1] and shared it with the class, of course this made it better by having others contribute. Some didn’t understand why I would “help others out” by giving it away, but I never understood that, like a page of formulae are going to get you an A (also why not help others out?).

Of course after spending so much time developing the formula sheet and working through the example problems (always the most important thing you can do), I think I looked at the sheet twice in 3 hours during the exam.

Also, Dr. Glen Takahara, this class and your instruction are one of my fondest memories at Queen’s!

[0] http://kje.ca/school/stat455/cheat2.pdf

[1] https://mast.queensu.ca/~stat455/

Nice touch: 4.15 FERMAT’S LAST THEOREM: ... General case when n>2 was proved by Andrew Wiles (1994). The proof is too long to be written here. See: http://www.cs.berkeley.edu/~anindya/fermat.pdf

I actually can't tell if that was an intentional "margin" joke, or if the author is just bluntly stating a fact about Wiles' proof...

EDIT: Nope, probably intentional. The author doesn't say something similar for any other proof based on a quick CTRL+F :)

Fermat wrote that in the margin of his book Arithmetica that a proof existed, but there wasn’t space in the margin to write it. It took Wiles 385 years to find a proof, and it won’t fit in a margin. https://en.m.wikipedia.org/wiki/Fermat%27s_Last_Theorem

That’s the allure of the theorem; that a simple unknown proof may exist.

Yes, I remember when news of his proof broke, being disappointed at how voluminous and obscure (to someone like me) it was. I'd been hoping for something I might be able to get my head around. (Hard as it was, I don't think Wiles spent 385 years coming up with it btw!)

Whether there is an existing and verified proof or not, there is still a great mystery to be solved by figuring out what Fermat actually meant by what he thought as an elegant solution, whether it is an actual solution or not.

Well, it could have been like Kempe's chains... they finally realized there is a problem, and then it took like 100 years before Appel and Haken made what is probably the first computer-aided proof. And who can say it's really a "proof" if it doesn't explain "why" it's true.

Phrased in a way that doesn't imply Wiles's extreme longevity: it took 385 years of advances in mathematics to invent the tools and frameworks that allowed Wiles to come up with the proof.

There's some speculation that fermat made the same mistake as lamé, who thought he had a proof. However lamé incorrectly assumed unique factorisation of a general number field, which was an easy mistake to make at the time.

> That’s the allure of the theorem; that a simple unknown proof may exist.

Well, Fermat made lots of similar claims wrt. other propositions, and for most of them the proof was found easily, or perhaps they were refuted altogether and shown to be wrong. FLT gets its name because it was a very rare case of a claim that just couldn't be solved, one way or the other. In fact, it seems that Fermat himself may have realized at some point that what he thought of as a proof he had, was in fact wrong - and dropped his claim altogether as a consequence. Which would then explain why it was only found as a margin note in a textbook. It's fascinating because it's such a simple claim to state, and yet the proof is incredibly complex. To be sure, logicians can predict that such cases will occur, in the abstract; it's a bit like having hard-to-solve instances of the SAT. But it's still nice to have such a natural example!

Yeah that's the math lore what I was referencing when I put the word margin in quotes :)

I wasn't sure if the author was making an intentional callout to Fermat's lost marvelous proof he couldn't fit in the margin. But indeed, looks like he was, since he doesn't seem to have really mentioned the length of any other proofs.

Link's unfortunately broken :(

You can find it at https://web.archive.org/web/20170414120550/https://people.ee...

I like the idea of this, but I'm not sure that "cheat sheet" is the best term for it, given that it weighs in at quite a few pages (191 physical).

"cheat ream" ?

Yes, cheat tome.

Cheat epic

Cheat codex

I believe that this sort of collection of tables is commonly called an “almanac”—but maybe only when the subject is of practical use.

The sort of ~100 page softcover reference book that we were permitted to use in highschool math, physics, and chemistry exams is called around here, literally translated, a book of tables. The term is probably a remnant from a time before pocket calculators when it contained actual trig and log tables. "Book of formulas" would probably be a more apt name nowadays. Not sure if there's a common word for such a thing in English.

This kind of thing? https://en.wikipedia.org/wiki/Abramowitz_and_Stegun

I'm not sure there's really an English word for it. That's strange.

I guess, but a very abridged version. It contains highschool-level things like trig identities, integration rules, fundamental physics and chemistry equations, values for various constants, and so on. It’s published by the national association of science teachers. The idea is making exams more about how knowledge is applied than rote memorization.

Normally, I've heard others reference books like A&S as a "handbook."

It's even in the formal title.

Right. Only "handbook" is so broad. It could be about any subject.

In Ireland, we literally called our reference book for exams "the log tables", despite there not having been any table of logs in any edition of it for quite a long time.

I got a B in probability because I didn't write a proof of the central limit theorem on the allowed cheat sheet for the final exam. So of course it's the first thing I looked for on this one. It's not there.

Aren't most proofs of the CLT pretty extensive?

There are a few short ones going from area integral comparisons.

The easiest is to look at characteristic functions and cumulants; for a random variable T with PDF p(t) we say T ~ p and define

φ_T[f] = ∫ dt p(t) exp(-2πift) = ⟨ exp(-2πifT) ⟩

If two variables X ~ r and Y ~ s are independent then you can prove [from ⟨f(X) g(Y)⟩ = ⟨f(X)⟩ ⟨g(Y)⟩ or X+Y ~ q where q(z) = ∫ dx r(x) s(z — x)] that their sum has a characteristic function

φ_{X+Y} = φ_X + φ_Y

And therefore the “sample mean” M of n IID variables is itself a random variable with characteristic function

φ_M[f] = ( φ[f/n] )^n.

So we find that

log φ_M[f] = n log φ[f/n] ≈ 0 + i a f – b f²/n + O(f³/n²).

These terms [a, b] from expanding the log of the characteristic function constitute the cumulant expansion and for large n the other terms shrink to zero, so that the characteristic function is to first order in 1/n a Gaussian.

The characteristic function was a Fourier transform of a PDF, so an inverse Fourier transform gets it back:

p(t) = ∫ df φ_T[f] exp(2πift)

But the Fourier transform of a Gaussian is just a Gaussian.

Surprise you can use those character like “∫ φ π”. Thought you need to say pig etc.

A B is like 80% or so, judging from A being the best iirc? I'm not familiar with alphanumeric grading systems.

Things can get a bit customized at either end of the spectrum, but generally each letter covers 15%, with A..D covering the span 100% to 40%.

So a B would be 70 to 85.

Shouldn't that sort of grading be on a bell curve? That would seem to be the fairest.

Many smaller (<60 students) math classes, in my experience, have bimodal distributions of scores, so a bell curve by definition simply doesn't make sense. In addition, there's been a move to standards-based or mastery-based grading, that is, grading according to what you know of the material rather than how you compare to your neighbor. This allows comparisons over time and consistency with regard to subsequent classes -- if you have a C as a prerequisite for the next class, then a C should indicate the same mastery of material rather than the same relative position in the class.

Based on my memory of what the teacher said in my statistics class in school, exam results in Scotland are normalized as z-scores vs that year's population. At least they were a zillion years ago.

Let's say that most math majors take this course in the first semester of their sophomore year. Then the bell curve grading gives you a much lower grade for identical work if you take the class in the first semester vs second semester. You also get a lower grade for going to a better school. You even get a lower grade for helping your classmates.

This makes the grades unfair and not useful for judging mastery of the subject. It only makes sense if the goal of a course is to beat the other students. For most courses, the goal should be learning.

Is this a new thing? I graduated highschool in 2001 and each grade letter was 10% and equated to a grade point.

    90%+ => A (4.0)
    80%+ => B (3.0)
    70%+ => C (2.0)
    60%+ => D or F depending (1.0 or 0.0)

At university, we only used grade points and they were very, very similar in scale.

It was the grading system in Ireland when I graduated secondary school. However, it looks like the meanings of the letter bands varies dramatically between countries.

70 - 85 for a B?! I wish I had that deal.

At my university the letter grades were

    A+  99.00 - 100.00%
    A   93.00 -  98.99%
    A-  90.00 -  92.99%
    B+  87.00 -  89.99%
    B   83.00 -  86.99%
    B-  80.00 -  82.99%
    C+  77.00 -  79.99%
    C   73.00 -  76.99%

Many places in the US, each grade covers 10%, so As (with plus or minus) go between 90 and 100, etc, with D from 60-70 and F below 60.

It's typically the 80-90% range. It's also typically divided into thirds for B-/B/B+. I actually got a B+, so it would have been closer to 90%.

Question asking for the central theorem proof in a probability class happened to me too. Not answering this one gave me an A, though.

More “Cheat Book” than “Cheat Sheet” :)

Looks like it could do with typesetting in LaTeX - I think the author started doing this here: http://mathscheats.weebly.com/ but never entirely completed it. Plenty there to chew on though.

Ah, 10% of the first section of the CRC Handbook of Chemistry and Physics, with amateur typography. Sort of like Greenspun's tenth rule, but for math.

I've heard of mathematicians handwriting proofs in the margins of books. Like an MVC, I can appreciate the data without appreciating the presentation.

While we're on the topic of this kind of thing: https://en.wikipedia.org/wiki/Synopsis_of_Pure_Mathematics

This is an excellent book, but perhaps a bit dated despite the fact that Mathematical Books have a long shelf-life. Factoid: The book is noteworthy because it was a major source of information for the legendary and self-taught mathematician Srinivasa Ramanujan who managed to obtain a library loaned copy from a friend in 1903...

It's awesome. Though I prefer my Bronshtein :D https://en.wikipedia.org/wiki/Bronshtein_and_Semendyayev

Russian version?

Bronshtein is excellent, but a bit dated. For me in particular it's lacking coverage of modern ideas on function approximation.

Also, it isn't free ;)

Interesting - I've had the German version from my university days (every ME student had one) and it's spelled "Bronstein". The English spelling makes me a little dizzy.

IIRC it does not cover probablity and statistics, a strange omission considering the Russian heritage.

When I was studying mathematical physics, my classmates and I made similar quick reference notes in latex. Based on a cursory look, it seems to be missing some important complex analysis and abstract algebra/lie theory results (although I haven't read what the author studied).

Searching for stuff I've used, this document is also quite light on combinatorics, complexity theory, and order theory (and of stuff I haven't used much, I don't see anything on category theory or topology). I don't think 330 pages is nearly enough to be truly all-in-one.

Agreed. This document is reasonably broad but it's missing quite a lot of undergrad mathematics, let alone graduate math.

If you literally wrote down sequences of definition, theorem, proof, definition, theorem, proof, ... with no exposition or exercises whatsoever, I think you might be able to include most undergraduate math in about 1000 pages. That would include calculus, real analysis, complex analysis, linear algebra, abstract algebra, discrete math. Maybe elementary number theory, topology and probability theory as well. That would be...horrible to learn from, frankly. Imagine a ten volume set of Baby Rudins, with no exercises.

If you really doubled down on the cheat sheet angle and didn't include any proofs - just the theorems, identities and inequalities - I think you could get through all undergrad math in a few hundred pages. But you wouldn't have any of the peripheral content the author included, like physics/economics.

'Riley, Hobson and Bence' was a standard reference I used throughout my undergrad and graduate studies. Sure enough, it's about 1200 pages.

Out of topic, but why is your username green?

I think it indicates new accounts. As of writing this comment the profile is only 1hr old.

Yep. Long time lurker on hacker news, but never felt the need to comment before. To be clear supernova's comment didn't trigger me - I just felt that it was worth pointing out that the document was not uncommon in my experience.

You know you're in for a head banging when the Table of Contents is 25 pages long! :o

https://archive.org/details/elementsquaterni00hamirich/page/... Hamilton's "Elements of Quaternions"'s table of contents is about 60 pages long and includes footnotes.

It is interesting and fun! I have a loose suggestion - it could be published together with LaTeX codes for any formula present - so it would be great speed up for someone who wants to use various formula in his works. However the choice of various areas is strange for me ( partially lack of some engineering areas, partially lack of very basic physics things, partially lack of mathematics) A lot of things is missing: Maxwell-Clerk equations. Einstein equations. Schrödinger equation. Dirac equations. Notable: Laplace equation and Maxwell-Clerk equations, wave equation!!! Harmonic oscillator equation. Quantum physics, Heisenberg relation at least please! Hydrodynamic, notable no Navier-Stokes equations. Special functions: Bessel, Jacobi, Lagrange, Chevyshev polynomials, various equations related to it. No elliptic functions, no Weierstrass function mentioned. No various number theory objects: Mobius function, Minkowski function ?() not mentioned. Congruences nearly omitted ( Chinese remainder theorem maybe) Group theory, some simple results from category theory, Shannon theory completely missing. No universal algebra. No basic cryptography. Complete lack of various numbering systems ( binary, hex at least)

Find a bug in page 39: y' is Lagrange's notation while dx/dy is Leibniz's.

Seems very similar to a classic formula collection like https://dlmf.nist.gov/

One day, I'll make an Anki version of this.

Just start with one small section :P

Last year, when I was in high school, I turned most of my math (and physics) textbook into an Anki deck :D

It's really good, especially when the final exam covers +4 years of mathematics.

I remember for Maths, Further Maths and Computing A-Levels typing in mini programs for everything into my TI-85, from stats to bubble sort or curvature. It took so long typing that on a numerical keypad I could remember everything and no longer needed it. Still, a good exercise in basic programming and not unlike remembering from a flashcard deck.

Four years later in banking, I discovered the entire industry does the same, but in Excel. Enjoy your studies!

Post it when you do! Might be worth making it open-source so not only one person has to do it :P

Speaking of, can anyone commend some good Anki mathematics decks?

There is just one link here: https://learnawesome.org/learn-awesome/mathematics.html

If people share links here, I'll send a PR to learnawesome to add those under mathematics#flashcards section.

First time I've seen someone use Keybase.pub. Last time I checked they gave out 250gb for free for everyone... this is a good use of that!

I wonder how long that can last before abuse kills the system. Some quotes from their page about KBFS [0]:

"The 250GB free accounts will stay free"

"we'll never run an ad-supported business"

"we're not trying to make money"

[0] https://keybase.io/docs/kbfs

Probably why they don't market it. If they did... like Dropbox, Dropbox would have to say goodbye to a lot of users, given that these users understand that Keybase doesn't have the efficiency or reliability that Dropbox has.

How is Keybase funded anyway? They say they’re hiring, so money is coming from somewhere.

Funding from Stellar: https://keybase.io/blog/keybase-stellar

Their Series A raised $10.8M back in 2015: https://keybase.io/blog/2015-07-15/keybase-raises-series-a

I remember using something similar called "Mathematics Handbook for Science and Engineering" in university. https://www.amazon.co.uk/Mathematics-Handbook-Science-Engine...

I assume there are many others, and this is a free alternative.

nice work. I would have removed

most of 'PART 1: PHYSICAL CONSTANTS', 'PART 8: APPLIED FIELDS', 'PART 18: ELECTRICAL', and some of 'PART 99: CONVERSIONS'.

"all-in-one" math seems enough :). Other stuff seems arbitrary and leaning towards physics (which could have its own giant book).

I'm biased as I'm an EE, but I'd say that the Laplace transforms within the Electrical section are firmly in the realm mathematics, so keep them. It just so happens that they are only really useful in the domain of digital signal/control processing, and I think to get the true form or radioactive decay(?) though I may be mistaken. I'd put it next to information on Fourier transforms. The circuit theory may be a bit unnecessary though I agree.

Things get kind of pixelated for me around page 123. Anyone else?

You are not alone. Seems like formula's are not vector anymore from page 121.

Add this to the list of items (or perhaps the only item?) you'd take if you'd time travel to the past

I've owned paper copies of Murray Spiegel's Schaum Outline of Mathematics, and even the government-funded Abramowitz-Stegun doorstop, this reminds me of those somewhat, but the title is misleading as it has as much physics and chemistry as mathematics.

Pages 168 to 262 seem to be missing?

Fermat’s Lost Theorem?

Really? That's odd -- I see pages 1-212 (213+ are missing).

OK, so, I also hate to be "that guy", but, despite the admirable effort put into creating this by the author, I am sad to say I don't see why some people are excited about this... Because unfortunately after just looking at a few pages, I saw lots and lots of error and misleading or plain confusing statements, basically on every single page I looked at closer, which makes me distrust it. Granted, these vary in their severity, but still...

Examples:

- p. 50, definition of a complex vector space, says " A complex vector space consists of the same set of axioms as the real case, but elements within the vector space are complex.". The vector space does not "consist" of the axiom, it adheres to them. And it makes no sense to say that the "elements" (vectors) are "complex". Rather, that scalars are allowed to be complex, not just real.

- p. 50: definition of a subspace is a mess. To pick just one obvious problem with it: What even are "axioms (a) and (b)"? Perhaps the three unlabeled "axioms" at the top of the page are meant (being closed under addition, additive inverses, and scalar multiplication)? But certainly the third one (axion "(c)"?) needs to be verified, too (whereas the second, about additive inverses, is redundant).

- p. 51 the examples at the top of the page end with mentioning C[a,b], the set of all continuous functions on an interval [a,b]. But then it claims that this is actually not an example, because "it has infinite dimensions". But really this is a perfectly fine vector space (also, we haven't even defined what a "dimension" is yet)

- p. 51, definition of linear independence says "c_1=c_2=c_n=0" which is missing a "=..." before the "=c_n"

- p. 52 the "general vector" given as a column vector doesn't make sense in a general vector space

- p. 53: "Matricis"

- p. 56 "Laprange's theorem" should be "Lagrange's theorem"

- p. 126: "EXPONETIAL"

- p. 167: "Matricies", "Prinicples", "opertaions",

- p. 168: "Determinate"; the formulas for 2x2 and 3x3 matrices implicitly assume a labeling of the entries which is never given, rendering this semi-useless

- one section is titled "MISELANIOUS"

And on page 38, the fields of real and complex numbers, R and C, are introduced as being written with a "blackboard" font (\mathbb), while on page 51 this is not followed (instead, we get \mathcal{R} and plain C). Why even introduce these conventions if they are then not followed?

Sure, many of these are minor and perhaps even "obvious" mistakes. But if you know the matter well enough to spot all of these, maybe you don't need this cheat sheet? Also, as a mathematician myself, my experience is that the number of spelling mistakes in a research paper (or in anything written and submitted by students) is a good first proxy for the quality of the text: if you can't be bothered to even run a spell checker on your text, should I really trust you to have verified all your computations and logical deductions carefully? (And no, I don't apply this to, say, posts here on HackerNews: I hate it when people shoot down a comment, or a twitter post, or whatever, just because it contains typo. But writing a book is a bit of a different affair, isn't it?).

Hence my point that I wouldn't want to suggest this to anybody as a reference. :-(

Page 33: PART 2: MATHEMTAICAL SYMBOLS

I hate how often these sprawly things are called cheetsheets:

  LOGIC SYMBOLS
  Symbol Symbol Name Meaning / definition Example
    &        and     x & y

Slightly off-topic: from a security perspective, how safe/not safe is it to be clicking open random pdf's? Wouldn't this be a possible avenue for malware?

Sure, but so is clicking open websites unless you have Javascript disabled, in which case half the web is broken for you.

https://github.com/osnr/horrifying-pdf-experiments

https://www.alchemistowl.org/pocorgtfo/

Yes. Not only is it possible but historically already an avenue of attack.

Awesome! It only serves to remind me I know practically nothing about Mathematics. "Good Primes" and "Happy Primes" .. who'd have thought it ...

To me this seems to be exclusively undergraduate mathematics that one might learn in an engineering program. No mention of topology or modern algebra.

It's organized like a debate file. Fascinating.

Reminds me of the old Schaum's Outlines, I still have a couple of them on the book shelf from college days, saved my bacon many times.

Uh, this is a book.

Missing the cheats for division (how to rapidly tell if a number is divisible by 3, 7, 2, 5, etc. for prime factorization.)

misprint PART 2: MATHEMTAICAL SYMBOLS

I really didn't want to be that guy, and props for the author for such comprehensive reference work, but god, what an appalling typography. Bad tables with too many lines bitmap formulas with misadjusted size, poor spacing, ugly font... Almost everything that could be wrong is wrong.

I came here to say the same thing. Looks like the author did not use a good authoring tool to produce good math output.

I generally take notes like this with LaTeX and compile them to PDF but PDFs can be large and if committing to a Git repo can lead to large .git directories. The BasicTeX package for Mac (brew install basictex) has worked well for me: http://www.tug.org/mactex/morepackages.html

These days I also take math notes as plain HTML files containing Markdown and LaTeX, then render with the TeXme one-liner here: https://github.com/susam/texme

I guess what the OP has done here is take all the notes in Word or some other WYSIWYG document editor not specialized for mathematical typography and converted the whole document to PDF. This won't lead to good results. It is absolutely necessary to use tools specialized for mathematical typography to write and publish math.

By the way, is there anyway to create high quality math distributables that are both self-contained and lightweight?

Why commit the output files? I generally put "*.pdf" in .gitignore.

Probably so that someone can download it without compiling it? GitHub Releases or an equivalent would probably be better, though.

That's right. I would like others as well as myself to be easily able to download the PDF files without having to compile it. I tried out GitHub releases and it works okay but not great. I cannot track all the compiled PDFs I have at a single place or move them easily from one system to another like I could with GitHub repos. I am also trying to avoid getting locked into a specific service like GitHub releases.

I have very good experiences with Gitlab CI: It just recompiles the PDF(s) from the repository within a minimal docker container (containing a full Tex Live repository) and pushes them online on a website (sFTP or similar). Also Gitlab allows to host the build assets.

Just as a note, MS Word has had LaTeX support for about 2 years now.[1]

1. https://blogs.msdn.microsoft.com/murrays/2017/07/30/latex-ma...

If I had only read this comment and didn't look into the PDF, I'd have thought it indeed have some appalling typography -- as opposed to some minor nitpicks I wouldn't even care about...

I felt the same. Also feel that he put too much stuff in, as if wanting to make it run for as many pages as possible.

This. Having an ~30 page TOC and no hyperlinks to the chapters/section irritates me to no end.

Not LaTeX; didn't read.

This, some formulas quite hard to read.

The first thing I look for in a math paper is whether the typesetting is up to TeX's standard. If it's not good enough, I'll just skim the text.

I'm not sure whether this pro-TeX prejudice is a good or bad thing...

I have to admit it's a pretty ugly manual.

Some of those formulas were really blurry, while some of the tables spanned weirdly over pages.

The hosting issues could have been fixed as well if it was LaTeX as it would have been neat in a git repository.

Gitlab also has continuous integration for LaTeX

* https://www.vipinajayakumar.com/continuous-integration-of-la...

* https://sayantangkhan.github.io/latex-gitlab-ci.html

Don't see any logic equivalencies... I think they are kind of neat!

Woof. Flashbacks to Sister Mary's Calculus class in 12th grade.

Quiet handy and amazing thank you very much for sharing this over.

Nice work.

But on page 43 "quadratic" is misspelled.

Why does the author not use LaTeX?

bet i could fit this on a 3.5in x 5in notecard...

s/Cheat-sheet/Cheat-book/g

Last page says "Page 212 of 330"

Pages 213+ are probably where they discuss cardinality.

It's a very fine compendium of notable relations.

At 212 pages long, it's certainly not a cheat-sheet.

If it didn't have obvious spelling errors I might be more confident the rest has been transcribed accurately.

Someday the cover will read e^iτ = 1 and all will be right with the world.

Some believe the pi version is superior due to the inclusion of three operators (+, *, exp), and five numbers (0, 1, i, e, pi) which are all fundamental in some sense. The tau version omits the + and the 0.

e^iτ + 0 = 1

Fixed.

e^iτ = 1 + 0

Fixed^2

e^iτ = 1 + 0i

Fixed for real this time-final.final.v2.docx

You mean fixed for all real values of i?

-1 not 1 ...

e^iπ+1=0 from

e^ix=sinx + icosx with x=π

Thats why we are using τ not π.

As the author of The Tau Manifesto, I’m well aware of this (pseudo-)argument, which is dealt with explicitly here: https://tauday.com/tau-manifesto#eq-euler_tau_zero

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